Yes, pea puffers need live plants. Pea puffers need a densely planted tank to thrive, otherwise, they will become stressed.
Pea puffers, especially male puffers, are highly territorial. The live plants act as hiding spots for them. This will give them a sense of security, allowing them to explore and establish their territories without worrying about one another.
For a pea puffer tank, include dense and tall aquatic plants, such as Java moss, Java fern, hornwort, and anacharis. Floating plants with long dangling roots, such as Amazon frogbit and water spangles, will also work wonders.